2017/05/23 by David Bachiller, Bachiller, David, Ferran Cedó +5
Materials Science · Mathematics · #Magnetism in coordination complexes #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.1705.08493
The problem of constructing all the non-degenerate involutive set-theoretic\nsolutions of the Yang-Baxter equation recently has been reduced to the problem\nof describing all the left braces. In particular, the classification of all\nfinite left braces is fundamental in order to describe all finite such\nsolutions of the Yang-Baxter equation. In this paper we continue the study of\nfinite simple left braces with the emphasis on the application of the\nasymmetric product of left braces in order to construct new classes of simple\nleft braces. We do not only construct new classes but also we interpret all\npreviously known constructions as asymmetric products. Moreover, a construction\nis given of finite simple left braces with a multiplicative group that is\nsolvable of arbitrary derived length.\n